Functions That Retain Their Form When Inverted Are linear functions the only functions that retain their form when inverted -i.e. an exponential function becomes a log function when inverted, a square function becomes...--prophetes.ai

Functions That Retain Their Form When Inverted Are linear functions the only functions that retain their form when inverted -i.e. an exponential function becomes a log function when inverted, a square function becomes a square root when inverted, but a linear function remains linear when inverted?

The functions in question are those whose _implicit_ equations are _symmetrical_ in _x_ and _y_. E.g., if $xy=a=$ constant, then $x(y)=\dfrac ay$ , and $y(x)=\dfrac ax$ . Or if $x^n\pm y^n=r^n$, then $x(y)=\sqrt[n]{1\mp y^n}$, and $y(x)=\sqrt[n]{1\mp x^n}$. Etc.